If you are a EU citizen, you need no work permit to teach in Poland nor any medical tests that I'm aware of.

There are other things that you will need however which the school may help you to acquire, they will definitely need, but is essentially your problem to deal with:

You will need to be part of the tax system, that is so the school can pay you - a NIP number - apply at your local tax office. Takes up to 4 weeks.

I can't remember what the system is nowadays but in order to get your NIP you may need to be registered in Poland or at an address. This can be done at the local council offices. Take someone to help you as officaldom in Poland either is grumpy, doesn't speak English and/or is extremely intolerant of foreigners (on any day with an 'e' in it).

At the same time your NIP is generated, your PESEL (your personal id number in Poland) is generated. This may or may not cost you money to actually receive. this number is not essential but useful.